Skydiving Without a Parachute

Photo: Eddie Keogh/Reuters

Actually, that title is incorrect. Gary Connery recently jumped out of a helicopter from 2,400 feet and landed without a parachute. Although he didn’t use a parachute, he still had one — you know, just in case. Another somewhat important piece of information: He was wearing a wingsuit — basically a suit that makes a human more like a flying squirrel.

Before I forget, let me make a quick comment about the image above. Notice the guy with the really nice video camera on the platform with the white shirt? Do you also notice that he is recording the landing with his phone? I just found that funny.

If you want a video, I think the best one is the view from the guy that followed him down.

So, how did he do this? Essentially, there are two things. First, the wingsuit slows him down a bit as well as allows him to “pull up” a bit before landing so that he is moving more forward than downward. Second, the boxes. The boxes allow Gary to stop over a larger distance. Larger stopping distance means smaller stopping acceleration. Smaller stopping acceleration means less chance of injury.

Video Analysis

You don’t come here for the simple explanation. You come for the video analysis, right? So, let me start with some details. Sky.com has lots of nice pictures and stuff. From that, I find that the box landing area was 12 feet tall, 350 feet long and 40 feet wide. You know, it’s funny. In looking for details of these boxes I found one site that said they were 40 feet wide, one said 45 and one said 50 feet wide. One site said the runway was 300 feet long. It seems like it wouldn’t be too hard to get this number right. But what do I know? Oh, Sky.com reports that 18,600 boxes were used and Gary started 1 mile away from the landing boxes.

For the video analysis, I will (as always) use the free and awesome Tracker Video Analysis tool. For this first clip, the camera is on the ground but pans and zooms as Gary comes in for a landing. You know what this means, this means that it isn’t so trivial to do a video analysis. Fortunately, Tracker has this feature called “calibration point pairs.” Essentially, this lets you focus on some object in the background to rescale the video for each frame. If you want to learn more, here is a quick screencast tutorial I created a while ago.

After that, I get the following for the horizontal and vertical position of the wingsuit jumper. Note that there are still some perspective errors since the camera is not exactly perpendicular to the direction of motion. It is a good start, though.

Fitting a linear function to the vertical data, I get a downward speed of about 7.5 m/s (16.8 mph). From the horizontal data, I get a speed of 20.7 m/s (46.3 mph). Crazy. Crazy that this is close to reported landing speeds of 15 mph going down and 50 mph going forward. These things never work out like that.

Next: Wingman Video. There was another video from a camera on a tripod that didn’t pan or zoom, but the perspective was just too out of whack to get it to work. This top (but moving) view should work out nicely. The camera is far enough away that Gary will be close enough to the boxes so that the boxes can be used to scale the video. Also, the wingman is high enough overhead that perspective doesn’t look like it will be too big of a problem.

Here is a plot of the motion of Gary in the direction of the landing boxes (horizontal).

This gives a speed of 38.5 m/s (86 mph). So, quite a bit faster than the data from the other video. Now, what about the vertical data? I do have one trick to get the vertical data — Gary’s shadow. The cool thing about shadows is that for this short time interval, the shadow angle is constant. If I know this angle and the position of the shadow, I can get the height.

Maybe this diagram will help.

From this I get the following expression for the height (y):

If the angle, θ, is constant (and the ground is flat) then the height of Gary is proportional to horizontal distance of the shadow from the point just below the jumper. For my analysis of the video, I put origin right at the corner of the box runway. If I just guess that Gary lands 6 meters away from the edge, I can get the x-value for the shadow.

If I want to get the vertical speed, I need to know this angle of the shadow. I can use the boxes and their shadows. The boxes should be 3.66 meters high and the shadow is about 4.06 meters long. This would give a shadow angle of 48°. Now I can translate my shadow data into height data.

This doesn’t include the motion all the way to impact. Why? Because the shadow shifts from the ground to the top of the box. Here is the data for the time the shadow is just on top of the boxes. Actually, I think this is better data — not as much perspective error. Here is the plot of Gary as he gets close to the boxes.

This puts the horizontal velocity at only 15.1 m/s (33.7 mph). Odd. But the nice thing about this plot is that you can see the change in speed after he collides with the boxes. OK, what about the vertical position. Here is a plot of the perpendicular position of the shadow (which is not the height).

The slope of this data is not actually the vertical speed. If I divide by the tangent of the shadow angle, this will do the trick. I don’t need to worry about the offset from the position of the wingsuit guy since that won’t change the slope. Doing this gives a vertical speed of 8.68 m/s (19 mph). This is pretty close to the value from the other video.

Impact Speed

One last thing. If he was moving downward with a speed of 19 m/s, what would this be equivalent to? How high would someone have to jump to get to this same speed (ignoring air resistance)? If I use the work-energy principle, I can write (assuming this jumper starts from rest and using a system of the jumper plus the Earth):

Wow. 18 meters (60 feet) is a bit higher than I expected. Well, I guess it wouldn’t be so bad if you land in these boxes. People have jumped from much higher distances and survived just fine.

Homework

You thought you were going to get out of here without homework? Sorry. Here are your problems.

If the Wingsuit man was indeed going 19 m/s in the vertical direction when he collided with the boxes and moved 2 meters down, what acceleration (vertical acceleration) did he experience?

Suppose you wanted to to land in the boxes with a maximum acceleration of 10 g’s. How deep would you have to travel into the boxes?

Measurements from the video show that Gary stopped in a horizontal distance of 8.5 meters. If he had an initial horizontal speed of 39 m/s, what was his horizontal acceleration?

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